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Paper Citation Record · LEDGER

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method

As of 13 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2411.16038.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2411.16038 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T13:43:13.998101Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

30 of 30 outbound references displayed

  • verified exact0
  • verified fuzzy16
  • unresolved14
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c51cec47-5d09-4889-b4f0-1267530938ce · outbound

This paper cites Ambrus, I.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Ambrus, I

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.770045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.812858Z digest=sha256:945e92a5f6c23449845713513beaf63460a632d7d9ce4919fb1fc514a81dd541

Observation 240e1d7f-86ab-4ae0-a666-9840e119d7d5 · outbound

This paper cites an unresolved cited work.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-12T13:43:14.751873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.822356Z digest=sha256:5e907716f2121a7fa13e1ae29fb8d4d326268358e09ce108c9a66a80537ae460

Observation b59bfce6-2524-417b-a54d-f60d982180a5 · outbound

This paper cites Böröczky, The problem of Tammes for n = 11, Studia Sci.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Böröczky, The problem of Tammes for n = 11, Studia Sci

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.726799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.827587Z digest=sha256:e762f4ceacfc1bc1844e64605dd35c76ae8ef29bff6cc29a1ca2465cbc09654c

Observation aff2ec02-0f7a-40e1-ad40-7338636293cf · outbound

This paper cites Boyvalenkov, S.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Boyvalenkov, S

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.699504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.834244Z digest=sha256:821ad9b532465d1d2d8048ef8f44c94e21c15f0cdb7f6823a1af0295c3b332cc

Observation c2e97eb6-79c4-419e-b8be-796bedb74abe · outbound

This paper cites Boyvalenkov and D.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Boyvalenkov and D

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.678204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.840591Z digest=sha256:8b2fcb3d7e2958d4a21a5a802aec370e10ec05915a2a347d910af7898440b533

Observation 69012a02-47ec-4988-8741-244c8984068f · outbound

This paper cites Brass, W.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Brass, W

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.658967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.850078Z digest=sha256:7524bda9c47930c7250fc7a3c74a6d7b7acd75c6d84ed3e4de551dc210ce31a3

Observation 7e574b0d-2890-4604-b664-441094215af9 · outbound

This paper cites an unresolved cited work.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-12T13:43:14.638912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.857223Z digest=sha256:9b172a8360fed83e167d381d738adfa90c89bf7f033e8cd59d51b62584cbfa14

Observation af69fb0a-6b1b-4753-a470-a6e80ddf7889 · outbound

This paper cites Cohn, Table of spherical codes, https://dspace.mit.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Cohn, Table of spherical codes, https://dspace.mit

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.620634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.862418Z digest=sha256:6ef0f448dcfc7e3e190905385888338fa87500282f1a6053b0448a8866cca715

Observation c282bbc4-fe15-4470-b483-417850df0fe4 · outbound

This paper cites Danzer, Finite point sets on S2 with minimum distance as large as possible, Discrete Math.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Danzer, Finite point sets on S2 with minimum distance as large as possible, Discrete Math

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.601457Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.869693Z digest=sha256:4635362c9a8a680522e98b8d867e28b078033eb07971566017291c813e75531f

Observation 9457bb93-cc99-40da-9ff2-89858db02df6 · outbound

This paper cites Delsarte, J.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Delsarte, J

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.573034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.876911Z digest=sha256:6585a19ca1f78eca954572fd2ff95806e64d624d89952be701fdf7f520042436

Observation 3e2c15ae-a19e-46b0-85e4-adec68c6906b · outbound

This paper cites Delsarte, Bounds for unrestricted codes by linear pr ogramming, Philips Res.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Delsarte, Bounds for unrestricted codes by linear pr ogramming, Philips Res

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.546511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.884002Z digest=sha256:8b4ae90047de098df7e43443f318c831a847f4ec789a2ee8fe5b57c2eddb5b84

Observation 091faad9-f95c-4fc5-8509-8b654c227d14 · outbound

This paper cites an unresolved cited work.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-12T13:43:14.513453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.889524Z digest=sha256:df5b42b4a34434f00e1db86d9b7478f959533d670f6dc2cb548db4972f68d19b

Observation 10389b7e-1782-4ad5-b742-8c48cb698f53 · outbound

This paper cites an unresolved cited work.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-12T13:43:14.485688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.894755Z digest=sha256:38e11b5771d9d0837c555cc517ab30283ef66b4b75518811574674611c255032

Observation a83de8a7-1252-4400-b05c-70824ca8220f · outbound

This paper cites Mackay, J.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Mackay, J

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.466220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.899958Z digest=sha256:163f7dda709ed26e8189c12a7b23a7c0e4af4110640b5735fb06bfa3ea3cfcc4

Observation afce7578-6ea9-4d99-b3fe-cf507e0869ff · outbound

This paper cites an unresolved cited work.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-12T13:43:14.444308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.905882Z digest=sha256:8f70eb6667a81217da7b3159697f3efae09cc73fbad4b97dff69a72ebb2ec9e6

Observation 5c15038d-9195-4b0e-8d0a-23e44d335a23 · outbound

This paper cites an unresolved cited work.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-12T13:43:14.423215Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.911873Z digest=sha256:80c5775d98960abc4b692f124043aee618ef190b4739c8a2dc04805120543f0d

Observation 4e6c8676-a15b-4e93-be22-08e94355e295 · outbound

This paper cites an unresolved cited work.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-12T13:43:14.395223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.918867Z digest=sha256:3f91f952e8bb08fd3556f568e3de403aa6ee9477a16e8ba0376a1ff810c219b9

Observation 469c249a-9b68-49f6-82b4-05e4fd8cda03 · outbound

This paper cites an unresolved cited work.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-12T13:43:14.374219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.924770Z digest=sha256:38d78b1703afc3dfa3c21e0431854c1917682caa9792f02fdc601c08d9a6ecfb

Observation 1ee4a6b3-f846-43e8-a480-8956e7566cc9 · outbound

This paper cites an unresolved cited work.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-12T13:43:14.351602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.930320Z digest=sha256:92e30d8209314f0454cb214fbea44a9ee3074d6645a246d710e0e46d7711065c

Observation ea746cd4-4e77-4690-8488-3b2ee27a787a · outbound

This paper cites an unresolved cited work.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-12T13:43:14.322843Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.939839Z digest=sha256:4c561c6f2f29e69a984d32d860023c254b74b6fe1ba21b29016b7eec06e0b55b

Observation e9d262de-797b-46a0-86d4-82c0d8ed53f4 · outbound

This paper cites an unresolved cited work.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-12T13:43:14.292402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.946162Z digest=sha256:0013dfd3cb27d5d2ecd6f3e482aa169546d72cca993d84ddc4f979d7b4ab0c36

Observation 99364888-2985-40aa-983e-9a6210210f65 · outbound

This paper cites Pfender, Improved Delsarte bounds for spherical cod es in small dimensions, J.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Pfender, Improved Delsarte bounds for spherical cod es in small dimensions, J

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.270075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.951782Z digest=sha256:98e92308576cabff9b0ed7274c43e471f8d30a0d9739185cd269538c02c9db6f

Observation 8ad47469-564f-46bf-8f5b-d94062e6aad7 · outbound

This paper cites Pfender and G.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Pfender and G

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.249322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.957944Z digest=sha256:0a28c11752a3512ac64b7c3c8e110cad0e338e2471c5a98911d0598d2e30f24c

Observation edbbb6bb-a748-4149-b50c-2f5ff807faa7 · outbound

This paper cites an unresolved cited work.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-12T13:43:14.228814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.963586Z digest=sha256:77bd98166fb68c20b427e0de20552ced73d54a96009d5aaac1298c640dede367

Observation 07888cf6-5dba-412f-aa93-b93257dc5066 · outbound

This paper cites Schütte and B.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Schütte and B

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.197221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.968797Z digest=sha256:3dc986314abf922f596ef79bd8fd3205c598943f80c3e13b6e449a8db55dcc27

Observation 9b4b16f7-c4b5-4454-9033-323043190681 · outbound

This paper cites an unresolved cited work.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-12T13:43:14.173842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.973887Z digest=sha256:a9b1f56f70d377b69feff1367693f5da9a52747ebe9317963a1b0660f1c6c60d

Observation 322dd168-a5d9-4250-94e9-5ce14de2eb6e · outbound

This paper cites Hárs, The Tammes problem for n = 10, Studia Sci.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Hárs, The Tammes problem for n = 10, Studia Sci

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.146148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.979487Z digest=sha256:35950e406b112d7d88eaac2c3003f99f69c0a1fc864707a48e8d1b64ba424d1c

Observation 37906af6-9c66-4941-8a68-72ff8789873e · outbound

This paper cites The Mathematical Foundation of Post-Quantum Cryptography.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method The Mathematical Foundation of Post-Quantum Cryptography

Reference 28

Resolution
unresolved
no resolver link, observed 2026-08-12T13:43:13.984904Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T13:43:13.984904Z digest=sha256:dd0ba0780b3990befd9ac4c8a980e8647c984f5835f11a75a5c03f46d15dd21c

Observation 98d78db7-2c86-4db3-bacc-86a932375fde · outbound

This paper cites Zong, Sphere packings, Springer-Verlag, New York, ( 1999).

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Zong, Sphere packings, Springer-Verlag, New York, ( 1999)

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.113310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.991783Z digest=sha256:0363a232aa90439f56b0c9397ea42cf1d473ae302ab7fcd2e1e42f614ec92b44

Observation c78b050a-523d-4298-9264-3037b8710144 · outbound

This paper cites Zong, The kissing numbers of convex bodies-a brief su rvey, Bull.

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method Zong, The kissing numbers of convex bodies-a brief su rvey, Bull

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T13:43:14.086329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T13:43:13.998101Z digest=sha256:236ba89287238e51353cd0b203d9d6556ba5fad3686b125f0fa4eff7c02186b7

Pith citing papers

No inbound Pith citation observations are available.